The restriction transports the residual of the fine grid to the coarser grid. The typical process averages the neighboring vales according to a stencil, like
This is the so called full weighting restriction, as used in the example of the multigrid workbench.
which turns out to be the natural restriction, when finite elements on a square mesh triangulation are used to discretize the operator.
In general, the choice of restriction as the transpose of interpolation plays an especially important role in the praxis and theory of multigrid methods.
Ulrich Ruede , Thu Feb 2 21:05:56 MEZ 1995
Updated by Craig C. Douglas